Even as Dickens begins The Mystery
of Edwin Drood in an opium den in London's East End, his focal
character — John Jasper, organist,
choirmaster, and solid member of the Church of England — is haunted by the image of "Cloisterham" (Rochester) and its
venerable cathedral: “An ancient English Cathedral Tower? How can the ancient English Cathedral tower be here! The well-known massive gray square
tower of its old Cathedral?” (Ch, 1).
The initial chapter in the April 1870 instalment of the novel asserts the dominance of
the Kentish cathedral in Jasper's thoughts:

That same afternoon, the massive grey square tower of an
old Cathedral rises before the sight of a jaded traveller. The bells are
going for daily vesper service, and he must needs attend it, one would
say, from his haste to reach the open Cathedral door. The choir are
getting on their sullied white robes, in a hurry, when he arrives among
them, gets on his own robe, and falls into the procession filing in to
service. [Chapter 1]

Dickens based his version of the old cathedral
on his boyhood memories and more recent
impressions of Rochester, a town still dominated by twin relics
from the middle ages, its cathedral and castle. Both,
Dickens notes, dominate the skyline and the psyche of Cloisterham.
Gradually, chapter by chapter and instalment by instalment, Dickens
brings The image of Rochester Cathedral into focus. In Chapter 5, "Mr.
Durdles and Friend," Dickens gives the reader an impression of this
other world and life of the drug addicted organist: “John Jasper, on his way home through the Close, is brought
to a stand-still by the spectacle of Stony Durdles, dinner-bundle and
all, leaning his back against the iron railing of the burial-ground
enclosing it from the old cloister-arches.” Later in that same chapter Dickens filters images of the cathedral's
precincts through two very different consciousnesses, those of the gruff
sexton Durdles and his street-wise "Deputy":

They have but to cross what was once the vineyard,
belonging to what was once the Monastery, to come into the narrow back
lane wherein stands the crazy wooden house of two low stories currently
known as the Travellers' Twopenny: — a house all warped and
distorted, like the morals of the travellers, with scant remains of a
lattice-work porch over the door, and also of a rustic fence before its
stamped-out garden; by reason of the travellers being so bound to the
premises by a tender sentiment (or so fond of having a fire by the
roadside in the course of the day), that they can never be persuaded or
threatened into departure, without violently possessing themselves of
some wooden forget-me-not, and bearing it off. [Chapter 5]

Indeed, the reader gleans most of the details of the Cathedral,
particularly of its mysterious crypts in which, implies Dickens, lies
the mouldering body of young Edwin Drood, from the surly, alcoholic
sexton whose entire being is so intimately welded to the mediaeval
edifice:

Durdles is a stonemason; chiefly in the gravestone, tomb,
and monument way, and wholly of their colour from head to foot. No man
is better known in Cloisterham. He is the chartered libertine of the
place. Fame trumpets him a wonderful workman — which, for aught that
anybody knows, he may be (as he never works); and a wonderful sot--which
everybody knows he is. With the Cathedral crypt he is better acquainted
than any living authority; it may even be than any dead one. It is said
that the intimacy of this acquaintance began in his habitually resorting
to that secret place, to lock-out the Cloisterham boy-populace, and
sleep off fumes of liquor: he having ready access to the Cathedral, as
contractor for rough repairs. Be this as it may, he does know much about
it, and, in the demolition of impedimental fragments of wall, buttress,
and pavement, has seen strange sights. He often speaks of himself in the
third person; perhaps, being a little misty as to his own identity, when
he narrates; perhaps impartially adopting the Cloisterham nomenclature
in reference to a character of acknowledged distinction. [Chapter 4]